Question

question
find the exact value of \\( \cot q \\) in simplest form.
(the image shows a right triangle with right angle at p, vertices o, p, q. op = 4, pq = \\( \sqrt{15} \\), oq = \\( \sqrt{31} \\))

Explanation:

Step1: Recall cotangent definition

$\cot Q = \frac{\text{Adjacent to } Q}{\text{Opposite to } Q}$

Step2: Label sides for angle Q

Adjacent to $Q$: $\sqrt{15}$, Opposite to $Q$: $4$

Step3: Substitute values into formula

$\cot Q = \frac{\sqrt{15}}{4}$

Answer:

$\frac{\sqrt{15}}{4}$